Please expain all steps

A bank account is opened with $$10,000$ at time $t=0$ years. The account pays interest at an annual rate of $4\%,$ compounded continuously; the account accrues interest at a rate of $0\mathrm{.}04p(t).$ Suppose the deposit rate is

$r(t)=900$ dollars per year, $0t<mn>2</mn>$

$r(t)=450$ dollars per year, $2t<mn>5</mn>$

$r(t)=350$ dollars per year, $t5$

Formulate an appropriate ODE with an initial condition, and solve using

the Laplace transform. Plot the solution for time $0t20.$